Cancer is a dynamic process that proceeds through the accumulation of genomic alterations. Large sequencing projects have illuminated the complex static landscapes of alterations across a large number of tumors. However, these studies have failed to address the dynamic nature of cancers. Understanding how tumors are shaped by selective pressures bears implications in therapies and prognoses. To address this issue we propose PITCH (Parsimony Inference of Tumor Clone Heterogeneity), a computational model that aims to uncover the evolutionary history of tumors using high throughput genomic data from cross-sectional studies. PITCH identifies traces of older clones and reconstructs possible histories of lesions. By combining the data from different patients, PITCH is able to capture statistically robust historical relationships between driver alterations in tumors and to represent these relationships as an evolutionary network. We will calibrate the approach in a longitudinal cohort of nearly 1,500 Chronic Lymphocytic Leukemia patients spanning a period of 12 years, along with 20 Glioblastoma Multiforme samples. We aim to extend and thus experimentally validate the approach using the large collection of Glioblastoma Multiforme and Low Grade Glioma in The Cancer Genome Atlas. We will be able to provide a robust computational approach that can be easily extended to any other tumor type where large cross-sectional data is available. Discovery of alterations associated to different phases, stages or therapeutic strategies could provide invaluable biomarkers for personalized approaches based on genomic data.